Tapering Spiral Gas Turbine with Polygon Electric Generator for Combined Cooling, Heating, Power, Pressure, Work, and Water

ABSTRACT

A tapering exponential spiral for a gas expander for work extraction or air cooling. A gas compressor to increase the pressure and temperature of air. The compressor-expander forms a single and simple structure. 
     A generator with a disk format using a circle of alternating polarity magnets to induce current in polygon solenoids. 
     A heat turbine, Firefly Electric, is small, simple, and efficient heat engine. 
     A heat pump, Firefly Air, for cooling, refrigeration, water capture, and heating. Solar power can be generated and stored as compress air. 
     A water purifier, Firefly Aqua, to desalinate water by solar power. Sunlight is concentrated by a sun tracking conic reflective surface onto a column of salty water. Solar photovoltaic power can be used to power a spiral compressor to condense low pressure steam. Also, we reuse solar heat by extracting the heat of compressing and condensing steam for evaporating more salty water under reduced pressure.

CROSS REFERENCE TO RELATED APPLICATION

The present application includes subject matter disclosed in and claimspriority to a provisional application entitled “A Tapering Spiral GasTurbine for Combined Cooling, Heating, Power, Pressure, Work, and Water”filed Feb. 2, 2016 and assigned Ser. No. 62/290,393 describing aninvention made by the present inventor, with improvements disclosed tothe Patent Cooperation Treaty Application Numbers PCT/IB2016/001359filed on Jul. 5, 2016, and PCT/CN2016/105462 filed on Nov. 11, 2016. Thesubject entitled “Polygon Electric Generator” was filed Feb. 27, 2017and assigned Ser. No. 62/460,264.

BACKGROUND Of INVENTION

The world needs clean air, water, food, energy, and transportation thatis accessible and equitable to all, not just for the developedcountries. Key to universal provisioning of these amenities istechnological advances that meet these needs of people where they are,supported by energy sources that are local and affordable, such as solarpower and bottled liquid petroleum gas.

We are facing global climate change due to the burning of fossil fuelcausing global warming and rising of sea level. Burning coal creates airpollution. Ground water is rapidly depleted. Global warming bringsextreme heat, requiring more air conditioning that uses more globalwarming fossil fuel. Transportation requires expensive petroleumproduct, causing chronic particulate pollution.

To mitigate energy shortage and climate change, we emphasize three shiftof focus. The first shift of focus is from energy generation to energyapplication. Energy generation is just a mean to the end comforts ofclean air, water, food, and transportation. Energy conservation oftenbrings more comfort.

The second shift of focus is from electricity to heat. We can use heatdirectly for space and water heating, and indirectly to generatecooling, water, cooking, motion, and then motion-induced electricity.Electricity is generated for lighting, communication, computation, andelectric transportation.

We should store energy close to the form it is used: heat energy in heatbath, pressure energy as pressurized gas, chill as condensed refrigerantor frozen matter, and electrical energy in chemical batteries. If smalland efficient turbines are available, we should store chemical energy asfuel.

The third shift of focus is local generation, storage, conversion, anduse of energy. We want to reverse the Edison utility model ofcentralized generation (CG) of electricity with grid distribution.

We invented technologies that integrate a disk micro-turbine with a diskgenerator. We call that Firefly technology, which is personal yet asefficient as large power plants. CG becomes unnecessary and is replacedby Personal Energy (PE) for mobile collection, storage, conversion, anduse of energy.

PE replacing CG brings us full circle in 4 phases of industrialrevolutions. The 1^(st) revolution centralized work production by largesteam engines. The 2^(nd) revolution electrified the world with large ACgenerators driven by steam engines. The 3^(rd) revolution ofmicro-electronics gave us global computing and communication networks.The 4^(th) revolution of MEMS (Micro-Electronic-Mechanical Systems)reverses the 1^(st) and 2^(nd) revolutions of CG to give us PE, makingall things local, small, and personal.

Firefly gives Combined Cooling, Heating, Power, Pressure, Work, andWater (acronym CCHP²W²).

Firefly can help industrialize poor countries, allowing people to beproductive where they are without electric or water grids. Half of theworld lives without reliable electricity or running water supply.

Key to CCHP²W² is an efficient micro-turbine powered by concentratedsolar power or internal combustion of gaseous fuel. Integrated with themicro-turbine is an efficient micro motor-generator.

Let us survey the history of heat engines and electric generators. Heroof Alexandria invented the first heat turbine 2000 years ago. Steamproduced in a boiler was ejected through nozzles in opposing directions,turning the hinged boiler. The Hero turbine was a curiosity exhibited inthe Alexandria Library.

In between Hero and the 1^(st) industrial revolution, wind and watermotion energy were harvested by means of turbines, literally a rotatingdevice such as a wind mill or a water mill. Blades or buckets obstructwind or flowing water, spinning the turbine to extract mechanical work.

The first powerful and practical steam engine was patented by James Wattin 1769. Steam from coal fired boiler drives a piston in a cylinder togive a significant force for pumping water, weaving textile, and drivingtrain. Steam driven locomotives brought people to cities. Centralizedmanufacturing was driven by steam engines. These Rankine cycle heatengines boil a liquid to create pressure to do work.

Stirling engine was patented by Reverend Stirling in 1816. He wasconcerned with the deadly pressure of steam boilers. Stirling enginesuse two cylinders, one for heating air and another for cooling air.Expanding air performs work. These Carnot cycle heat engines operate athigh temperature.

Around 1830, Michael Faraday invented the homopolar disk generator.Electric current is collected from the perimeter of a rotating disksandwiched between poles of a C-shaped magnet. Lossy eddy current flowswithin the rotating disk. Despite improvements such as that by NikolaTesla, this generator was not used for utility power generation due tolow efficiency and voltage.

Inventions of Edison and Tesla created the power utilities in the early20^(th) century. Coal fired steam engines generate electricity byTesla's AC generators. Steam engines are large and inefficient. They arestrong but slow. To generate large current, AC generators require largeelectromagnets.

Nikola Tesla invented the 3 phase electricity generator with mutualinduction of current in stator and rotor coils. Ease of voltageconversion allows efficient high voltage transmission of electricityover long distance electric grid with much reduced ohmic loss of power.Power utilities adopt AC over DC.

Nikola Tesla also invented the Tesla turbine. The turbine comprises 3stack of closely spaced disks. Steam is injected tangentially on turbineperiphery. Steam spirals inward in between disks towards the center ofthe stack. Steam drags disks by gas viscosity. Tesla claimed to achieve90% isentropic efficiency of theoretical Carnot cycle efficiency, whichis not verified even with today's technologies.

Since 1950, gas and steam turbines have made power utilities much moreefficient. Steam turbines powered by steam generated by burning coalhave efficiency around 40%. Large amount of water is required tocondense low pressure steam from the steam turbine. Combined cycle gasturbine (CCGT) achieves efficiency above 60%. CCGT uses natural gas todrive a Brayton cycle gas turbine. Hot gas exhaust generates steam topower a Ranking cycle steam turbine.

Since the 21^(st) century, the world confronts pollution from burningfossil fuel. The resulting climate change is threatening human survival.Yet much of the world population remains poor for being served water,heat, chill, food, and transportation. CG is failing poor countries thatlack power infrastructure. Yet poor people suffer the most from globalwarming, rising sea levels, and chronic air pollution.

Burning more coal is not the answer to help people live a comfortablelife. We cannot afford to build expensive, polluting, and wastefulinfrastructure of energy collection, generation, and distribution.Natural gas and solar power are our energy source of choice for PE. Bothare abundantly available for personal energy generation and use. PE isefficient, clean, local, small, useful, and therefore beautiful.

To solve the energy and environmental crises, we have to personalizeenergy production, storage, conversion, and usage. We will focus onheat, as our energy source. Heat can come from solar thermal,geothermal, or from burning of piped natural gas and propane transportedin canisters.

Our goal is to make small gas turbines as efficient as large gasturbines, at a small fraction of cost per Watt of power. We wantcogeneration of heat, chill, water, and work besides electricity.

We investigate the geometry of open gas flow in spiral gas channels thatallows gradual release of gas pressure to produce work. We want to avoida sudden conversion of pressure into kinetic energy of the gas by meansof a tapering exponential spiral. The same spiral gas channel rotatingin a reversed direction can also be used as a gas compressor, increasingthe pressure and temperature of gas.

We investigate the geometry for electricity generation with modernmagnetics and electronics. Most electric generators and motors are polarin the sense of having multiple magnetic poles in the stator interactingwith multiple magnetic poles in the rotor. We assume a distinctlydifferent geometry of a polygonal winding without poles. The polygoncorners include a varying amount of magnetic flux as the polygon rotatesin the circle of magnets of alternating polarity. An electric voltage isinduced in the polygon solenoid per Faraday's induction law that inducedvoltage is the rate of change or included flux.

We propose three applications based on our invention of micro-turbineand micro-generator. First, we describe a heat turbine that integratesthe spiral compressor, the spiral expander, and our electric generator.This heat engine called Firefly Electric generates work and electricity.

This micro-turbine can be used to drive cars, directly powering thedrive train or indirectly with its electricity generated. The turbinecan be modified as a turbo charger for automobile piston engines, usingtailpipe exhaust to turn a spiral expander which then drives a spiralcompressor to increase engine pressure. Firefly Electric can also beused to fly drones. It can power homes by solar and gas energy.

The second application is a heat pump of a spiral compressor of airdriven by our electric motor to compress air. Heat of compression isused to heat water. Compressed air when cooled gives out water.Compressed air when expanded gives dry and cool air for air conditioningand refrigeration. Expansion of compressed gas can produce work forgeneration of electricity. The technology is called Firefly Air.

The third application is a solar powered water desalination systemcalled Firefly Aqua. We track the position of the sun, concentratingsunlight by a conic reflective surface onto a cylindrical water tank.Solar energy boils salty water under reduced pressure. Solar energydrives our spiral compressor to condense steam. Firefly Aqua has highefficiency as heat of compression and condensation is reused toevaporate more salty water.

SUMMARY OF INVENTION

The exponential spiral tapering outwardly is an effective geometry forgas flow for the conversion of the internal energy of pressurized andhot gas into motion energy. We solved the temperature and pressure dropof adiabatic gas flow in the spiral outwardly, pushing the turbine toyield motion energy.

The same exponential spiral tapering inwardly when turned in reversedrotational direction can be an effective geometry for compression ofgas, converting motion energy into pressurized and heated gas. We solvedthe pressure gain of gas by the spiral wall pushing gas toward thecenter.

We invent an electric generator based on the relative rotational motionbetween a circular set of axially magnetized magnets of alternatingpolarity with a polygonal solenoid. The magnetic flux of the magnetsthrough the polygonal solenoid changes as a sinusoid with relativemotion between stator and rotor of the generator. This changing magneticflux induces an electric potential between the two ends of the solenoid,thus converting rotational power into alternating current (AC) power.The use of three triangular solenoids to form a nine-point star cangenerate three-phase AC electricity. These generators can also be usedas motor generating motion from electricity. The circular magnets canalso be replaced by a conductor disk, making an induction motor orgenerator. Cascade of motor-generator can be used as transducer of ACfrequency and voltage.

We integrate the spiral compressor and spiral expander with thegenerator and motor for three applications. The first application calledFirefly Electric is a heat turbine that can convert solar or gascombustion heat into work and electricity. This heat turbine andelectric motor can drive vehicles such as cars, bus, trucks, trains, andsmall aircrafts. It can also be used to power and heat homes.

The second application called Firefly Air is a heat pump powered by amotor to compress humid air to higher temperature and pressure. Thecompressed air is cooled at room temperature to remove heat and humidityto produce heated water and moisture condensed potable water. Cooled anddried compressed air can expand in the spiral expander to yield work andcold air for air conditioning.

The third application called firefly Aqua is a solar water desalinationsystem. Focused sunlight from a sun tracking conic surface heats saltywater to boil at less than 100° C. in reduced pressure. Low pressuresteam at head of the heated water column is compressed by the spiralcompressor using solar power. Condensing higher pressure steam exchangesits heat of compression and condensation to further heat the salty watercolumn, generating more low pressure steam for even more potable water.Potable water is collected at the bottom beneath the column ofevaporating salty water.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 A tapering exponential spiral (top), expander with anticlockwisespirals rotating clockwise (bottom left), and compressor with clockwisespirals rotating clockwise (bottom right)

FIG. 2 Gas temperature drop ratio T/T₀ versus radius r and the Braytoncycle

FIG. 3 Gas compression ratio p₀/p versus radius r and the Hui cycle

FIG. 4 Polygon electric generator (FIG. 4a ), polygon induction motor(FIG. 4b ), rectangular electric generator (FIG. 4c ), and polygontransducer for frequency and voltage (FIG. 4d )

FIG. 5 Vertical view of turbine and generator cross section (center) andhorizontal cross section views of expander (top spiral disk) andcompressor (bottom spiral disk)

FIG. 6 Cross section view of a beat pump for heating water and airconditioning

FIG. 7 Cross section view of a solar powered desalination system usingspiral compressor

FIG. 8 A conic mirror concentrating sunlight onto a water column at thefocal line

FIG. 9 A scrolling compressor in open (when spirals are closesttogether, top picture) and closed positions (when spirals are farthestapart, bottom picture)

THE TAPERING EXPONENTIAL SPIRAL

Additional means to compress or expand a gas predominantly use twodevices: pistons or fan blades. Gas is enclosed in a cylinder with amovable piston to compress or expand the gas. Gas can also be struck byhigh speed rotating blades for imparting or harvesting kinetic energy ofgas.

We 3D printed turbines to find the appropriate geometry of spiral gasflow channel. We changed spiral size and shape. We tried the Archimedesspiral with radius r=aθ+b that increases linearly as turn angle θ.Testing with pressurized gas showed that the Archimedes spiral did notwork well.

We also tried the exponential spiral, also known as the Bernoulli spiralnamed after its inventor. Spiral radius r=ae^(bθ) increasesexponentially as the angle θ. We 3D printed a long and narrowexponential spiral with many turns, it spun well but created very littletorque. By tapering an exponential spiral of shorter length as shown inFIG. 1, we generated significant torque.

Exponential spiral occurs often in nature such as seashells and plants.Fluid dynamics gives rise to an exponential spiral shape for hurricanes.Galaxy arms are exponential spirals. The exponential spiral results fromthe physics of growth. Growth is often self-generating and self-similar.

The exponential spiral is self-similar: the spiral looks similar as wezoom into the center of the spiral. A spinning Bernoulli spiral does notappear visually contracting or expanding.

This self-similarity is due to an important property of the Bernoullispiral: spiral tangent makes a constant angle with spiral radius. Gasflowing in the Bernoulli spiral pushes against spiral wall at a constantangle. In contrast, the Archimedes spiral pushes against spiral wallwith diminishing angle.

An eagle circles and zooms in on a prey in a similar manner. The eaglefixes its eye on the prey. The line of sight of the eagle towards theprey is at a fixed angle. Distance of eagle from prey decreaseslogarithmically as the eagle turns. This logarithmic spiral is theinverse of the exponential spiral.

Exponential spirals have radius r=ae^(bθ) where θ is the polar angle inradians. Logarithmic spirals have

$\theta = {\frac{1}{b}\ln {\frac{r}{a}.}}$

We will use the relation

$\frac{dr}{d\; \theta} = {{abe}^{b\; \theta} = {br}}$

for change of variable from θto r. Spiral tangent makes a constant angle

$\alpha = {\tan^{- 1}\left( \frac{1}{b} \right)}$

with the radius. Spiral length from r=a is

$x = {\frac{\left( {r - a} \right)}{\cos (a)}.}$

FIG. 1 shows a spiral with outside wall that is an exponential spiral.The width between the outside wall and the inside wall is shown to betapering. Spiral channel width decreases exponentially as angle θ. Wewill show that this tapering is key to retaining gas pressure withoutrapid speeding up of gas.

Temperature Change for Adiabatic Expansion of a Gas in a Tapering Spiral

Key to our invention is simple solution for gas temperature as gasexpands adiabatically. In a tapering exponential spiral. This provesalso a high thermal to motion energy conversion efficiency.

Early on, we experimented with pressurized air driving a long spiral ofnarrow constant width. The turbine was spinning fast but produced littletorque. Torque force is important for work production.

Torque is produced by pressure force. To maintain better control ofpressure release, we consider varying the bore area A=wd, the width wtimes depth d of the spirals. Gas speeds up due to its internal pressuregradient as dictated by Navier-Stokes equation. Tapering prevents gasspeed up because of gas back pressure. We will show that this taperingmoderates pressure release.

This large torque is due to first a larger area of the outside spiralwall than the inside wall and second a larger leverage due to differencein the wall radius from the center of the spiral.

A high pressure and hot gas moving inside the spiral has two maincomponents of energy. The first component is gas internal energy due toheat, which is the chaotic motion of gas molecules.

The second component is gas kinetic energy, which is the systematicvelocity of gas. At the center of the spiral where a high pressure gasis heated, gas internal heat energy is high. Gas velocity is low.

Most micro-turbine designs use a nozzle to release immediately gaspressure, converting the internal energy of gas instantaneously intokinetic energy. Gas cools rapidly. Post nozzle, the high speed gasrapidly becomes turbulent. High speed gas makes impact on turbineblades, producing very little torque force. Most kinetic energy of thegas is converted back into heat, not work.

We strive not to reduce gas pressure suddenly. We use pressure force ofhigh temperature gas with retained pressure to produce a significanttorque force at lower angular velocity of the turbine.

Gas kinetic energy density is

${\frac{1}{2}\rho \; v^{2}},$

where ρ is the mass density of the gas and ν its velocity. For

${{\rho \text{∼}1\mspace{14mu} {kg}\text{/}m^{3}\mspace{14mu} {and}\mspace{14mu} v} = {100\mspace{20mu} m\text{/}s}},{{\frac{1}{2}\rho \; v^{2}\text{∼}5,000\mspace{14mu} {Pa}} = {0.05\mspace{14mu} {bar}}},$

about 5% of atmospheric pressure.

Gas internal energy density is pressure

$p = \frac{nRT}{V}$

according to ideal gas law. Our turbines operate at pressure beyond 10bars. Thus gas pressure far exceeds kinetic energy density.

Bernoulli's law states

$p + {\frac{1}{2}\rho \; v^{2}}$

is constant. For our turbine, pressure is converted to work before gasspeeding up. We will ignore kinetic energy component in energyconservation consideration.

We consider torque produced by pressure acting on turbine walls. Torqueis pressure p times spiral wall area

$\frac{r\; {\delta\theta}}{\sin \; \alpha}d$

times the leverage r cos α of the torque, where tan

$\alpha = {\frac{1}{b}.}$

Net torque is the difference between the greater torque force on theouter wall of the channel than its inner wall.

Net torque between the outside and inside walls is

${\delta \; T_{p}} = {{\left( {p \times \frac{r\; {\delta\theta}}{\sin \; \alpha} \times d \times r\; \cos \; \alpha} \right) - \left( {p \times \frac{\left\lbrack {r - w} \right\rbrack \; {\delta\theta}}{\sin \; \alpha} \times d \times \left\lbrack {r - w} \right\rbrack \; \cos \; \alpha} \right)} = {{{pbwd}\left\lbrack {{2r} - w} \right\rbrack}{\delta\theta}}}$

For a turbine rotating at angular velocity ω, this differential torqueproduces a differential power;

${\frac{{dT}_{p}}{d\; \theta}\omega} = {{{{pbwd}\left\lbrack {{2r} - w} \right\rbrack}\omega} = {{{pbA}\left\lbrack {{2r} - w} \right\rbrack}\omega}}$

This derivation made the following assumptions. We ignored gas kineticenergy and viscosity of gas flow. We assume pressure force is expendedas work rather than used to speed up gas. We also assume a constantpressure and velocity of gas across the radial width of the thin spiralchannel.

We now consider power flow of gas inside the spiral. Consider thepressure energy component P_(f) of gas flow. Pressure power flow acrossarea A of a gas flowing with velocity μ is P_(f)=Aup.

By conservation of energy, power loss P_(f) is power gain by theturbine. Therefore

${\frac{{dP}_{f}}{d\; \theta} + {\frac{{dT}_{p}}{d\; \theta}\omega}} = {{{\frac{d}{d\; \theta}({Aup})} + {{{pbA}\left\lbrack {{2r} - w} \right\rbrack}\omega}} = 0}$

Conservation of mass flow implies constant Aup. Dividing above equationby Aup gives

${{\frac{d}{d\; \theta}\left( \frac{p}{\rho} \right)} + {\left( \frac{p}{\rho} \right)\frac{\omega}{u}{b\left\lbrack {{2r} - w} \right\rbrack}}} = 0$

Change of variable from θ to r using the relation

$\frac{dr}{d\; \theta} = {br}$

gives:

${{\frac{d}{dr}\left( \frac{p}{\rho} \right)} + {\left( \frac{p}{\rho} \right){\frac{\omega}{u}\left\lbrack {2 - \frac{w}{r}} \right\rbrack}}} = 0$

From ideal gas law pV=nRT, we have

$\frac{p}{\rho} = {\frac{nRT}{\rho \; V} = {\frac{RT}{\rho \; {V/n}} = {\frac{R}{m_{w}}T}}}$

Molar mass m_(w) is the weight of a mole of gas. Thus p/ρ measures thetemperature T of gas.

With these substitutions, we obtain the remarkably simple differentialequation

${\frac{dT}{dr} + {T{\frac{\omega}{u}\left\lbrack {2 - \frac{w}{r}} \right\rbrack}}} = 0$

The first term is heat energy loss of gas across the radius. The secondterm is work gain by turbine.

We assume that gas flow is adiabatic, implying constant. TV^(γ−1). Gasvolume V is proportional to Au of gas flow velocity it across area A.Thus T(Au)^(γ−1)=T₀(A₀u₀)^(γ−1), giving

${\frac{dT}{dr} + {\omega \frac{T^{\gamma/{({\gamma - 1})}}}{T_{0}^{1/{({\gamma - 1})}}}{\frac{A}{A_{0}u_{0}}\left\lbrack {2 - \frac{w}{r}} \right\rbrack}}} = 0$

We choose A=wd with constant w and changing depth

${d = {d_{0}\frac{1 - {cr}}{1 - {cr}_{0}}}},$

a linear tapering of depth versus radius r of the channel. Note d=d₀ forr=r₀. Since radius and length of the spiral channel increaseexponentially as angle θ, channel depth d decreases exponentially aschannel length

$x = {\frac{\left( {r - a} \right)}{\cos (\alpha)}.}$

With this channel geometry we obtain the differential equation

${\frac{T^{{- \gamma}/{({\gamma - 1})}}}{T_{0}^{{- 1}/{({\gamma - 1})}}}{dT}} = {{{- \omega}{\frac{d}{d_{0}u_{0}}\left\lbrack {2 - \frac{w}{r}} \right\rbrack}{dr}} = {{- {\frac{\omega}{\left( {1 - {cr}_{0}} \right)u_{0}}\left\lbrack {2 + {cw} - {2{cr}} - \frac{w}{r}} \right\rbrack}}{dr}}}$

The initial condition is by T=T₀ when r=r₀. The solution of thedifferential equation is

$T = {T_{0}\left\{ {1 + {\frac{1}{\gamma - 1}{\frac{\omega}{\left( {1 - {cr}_{0}} \right)u_{0}}\left\lbrack {{\left( {2 + {cw}} \right)\left( {r - r_{0}} \right)} - {c\left( {r^{2} - r_{0}^{2}} \right)} - {w\; \ln \frac{r}{r_{0}}}} \right\rbrack}}} \right\}^{- {({\gamma - 1})}}}$

FIG. 2 is a plot of temperature T/T₀ dropping across turbine versusradius r₀=1 cm≤r≤r₁=4 cm for ratios

$\frac{\omega}{u_{0}}$

of 0.2, 0.4 0.6, 0.8, and 1.0. We choose r₀=1 cm, d₀=2 cm, maximumspiral radius r₁=4 cm, c=0.2, w=0.3 cm, and γ=1.4.

Efficiency is

${ɛ = {1 - \frac{T_{L}}{T_{H}}}},$

with T_(H)=T₀ the high post combustion temperature and T_(L) the lowexit temperature of gas.

${{{At}\mspace{14mu} \frac{\omega}{u_{0}}} = 1.0},$

efficiency is as high as 60%, at ω=377 rad/s (60 Hz), u₀=377 cm/s, abreezy speed (less than 15 kilometers per hour). Gas cools from 1000K to400K (127° C.).

Pressure Change for Compression of a Gas in an Exponential Spiral

The exponential spiral expander when turning in a reversed directioncompresses gas instead of expands gas. For adiabatic gas expansion,p^(1−γ)T^(γ) is constant. Using this constancy, pressure p at radius rof the spiral can be derived from the temperature drop equation.

Pressure increase p₀ is given by:

$p_{0} = {p\left\{ {1 + {\frac{1}{\gamma - 1}{\frac{\omega}{\left( {1 - {cr}_{0}} \right)u_{0}}\left\lbrack {{\left( {2 + {cw}} \right)\left( {r - r_{0}} \right)} - {c\left( {r^{2} - r_{0}^{2}} \right)} - {w\; \ln \frac{r}{r_{0}}}} \right\rbrack}}} \right\}^{\gamma}}$

A centripetal gas pressure is a result of gas flow towards the centerwith velocity u₀.

If gas flows outwards with negative u₀, pressure p increases towardsdisk periphery instead. That outward gas compression is a centrifugal:compressor used for the first jet engines invented during World War 2.Unfortunately, centrifugal compressors produces small pressure increasesfor its radial and centrifugal flow of gas. Later development of jetengines favors an axial instead of radial flow of gas through multiplestages of turbine blades that increase gas pressure from stage to stage.

We believe that centripetal compression is better than centrifugalcompression for achieving a high compression ratio, which leads tobetter turbine efficiency. For centripetal instead of centrifugal gascompression, compressor turns in reversed direction pushing gas towardsthe center. The gas spiral must be tapering towards the periphery ofturbine in order to trap gas inside spiral to move towards the center.Gas flow slows down towards the center, converting its kinetic energyinto pressure energy. Tapering reduces flow velocity u₀ at the center,increasing the ratio

$\frac{\omega}{u_{0}}$

which is important for increasing compression ratio

$\frac{p_{0}}{p}$

in the above equation.

We describe here the multi-staging of radial compressors. A taperingexponential spiral expander (bottom left of FIG. 1 with anti-clockwisespiral turn) is placed on top of a tapering exponential spiralcompressor (bottom right of FIG. 1 with clockwise spiral turn). We canuse the inter-spiral space of both the expander and compressor forfurther compression of gas.

We devise gas flow direction as follows. Gas flows in between thetapering spirals in the spiral compressor from outside to inside.Halfway through, gas flows into the space in between the taperingspirals in the spiral expander. Gas flows from inside to outside in thatspace, with gas sped up by centrifugal force. At the periphery of thespiral expander, gas flow into the tapered end of the spiral compressorchannels. Gas emerges at the center of the compressor triply compressed.The order of compression is first a tapering centripetal compression,followed by a centrifugal compression and finally by a centripetalcompression.

Multiple staging of compression with cooling between stages reduces gastemperature. We considered isothermal gas compression requiring heatexchange between gas and environment. Isothermal gas compressionrequires less energy than adiabatic gas compression. Heat loss ofpressurized gas facilitates cooling when gas expands.

For isothermal processes, work done dW_(T) to compress gas generatesheat dQ with

$Q = {{dW}_{T} = {{{nRT}\; \ln \frac{p + {dp}}{p}} = {{nRT}{\frac{dp}{p}.}}}}$

This heat is transferred to environment. Energy conservation implies

${{T{\frac{\omega}{u}\left\lbrack {2 - \frac{w}{r}} \right\rbrack}} + {\frac{T}{p}\frac{dp}{dr}}} = 0$

For isothermal processes, pV=nRT is constant for constant T. Velocity usatisfies the condition that Aup=A₀u₀p₀ is a constant for given valuesA₀, u₀, p₀ The above differential equation becomes:

${- \frac{dp}{p^{2}}} = {\frac{A}{A_{0}}\frac{\omega}{u_{0}}{\frac{1}{p_{0}}\left\lbrack {2 - \frac{w}{r}} \right\rbrack}{dr}}$

Solving the above differential equation with a tapering factor c, wehave the pressure ratio:

$p_{0} = {p\left\{ {1 + {\frac{\omega}{\left( {1 - {cr}_{0}} \right)u_{0}}\left\lbrack {{\left( {2 + {cw}} \right)\left( {r - r_{0}} \right)} - {c\left( {r^{2} - r_{0}^{2}} \right)} - {w\; \ln \frac{r}{r_{0}}}} \right\rbrack}} \right\}}$

This pressure increase is much less than that for a spiral that tapersinwards. FIG. 3 plots pressure ratio for isothermal compression, for rin the range r₀=2 cm≤r≤r₁=16 cm for ratios

${\frac{\omega}{u_{0}} = 0.05},0.10$

0.15, 0.20, 0.25. Tapering factor is c=0.025 and width w=1 cm. Theunknown exit velocity u₀ is determined by pressure at the two ends ofthe spiral, namely p₀ and p₁. Velocity u₀ will adjust to become thesolution of the above equation for given

$\frac{p_{0}}{p_{1}}.$

Pressure increases linearly as the angular velocity ω and compressorradius. Compression increases as flow velocity u₀ slows. More work isdone to compress a slowly flowing gas. Flow velocity u₀ is related torim flow velocity u₁ by the conservation of flow equation A₀u₀p₀=Aup forisothermal compression. Substituting

$\frac{p_{0}}{p} = \frac{Au}{A_{0}u_{0}}$

into the pressure ratio equation:

$u_{0} = {{\frac{1 - {cr}}{1 - {cr}_{0}}u} - {\frac{\omega}{1 - {cr}_{0}}\left\lbrack {{\left( {2 + {cw}} \right)\left( {r - r_{0}} \right)} - {c\left( {r^{2} - r_{0}^{2}} \right)} - {w\; \ln \frac{r}{r_{0}}}} \right\rbrack}}$

For c=0, isothermal compression reduces velocity as

$u_{0} = {u - {{\omega \left\lbrack {{2\left( {r - r_{0}} \right)} - {w\; \ln \frac{r}{r_{0}}}} \right\rbrack}.}}$

A New Electric Generator and Motor

We invent electric generator and motor that have the same disk formfactor of our spiral turbine. Pioneers such as Edison, Tesla, andSteinmetz were frustrated by technology available then. The firstproblem was the lack of strong permanent magnets. Lacking strongpermanent magnets, large electromagnets were used to induce electricity.The second problem was the lack of high speed heat engines such as themodern gas turbine. Magnets have to be strong to convert the slow butlarge torque of steam engines. The third problem was the lack of solidstate electronics for digital and solid state control of voltages andcurrents.

Modern technology solved these problems. Rare earth magnets give strongmagnetic field. High speed turbines run much faster than piston steamengines. Solid state high power electronics provides flexible control ofvoltage and current. Digital electronics can synthesize variablefrequency, phase, and amplitude of AC. Our generator is simpler and morecompact than Faraday's or Tesla's.

FIG. 4a illustrates how electricity is induced in 3 triangular solenoidsby the relative motion of the circle of 6 magnets of alternatingpolarity. A circle of magnets induces electricity in polygonal solenoid.Magnetic flux through the solenoid changes as a sinusoid. Inducing anelectric potential between the two ends of the solenoid according toFaraday's Induction law to convert motion into alternating current.

The polygon for the solenoid can be a triangle, square, rectangle, orpointed star, etc. The polygon includes changing magnetic flux as itrotates coaxially with a magnetic circle of alternating poles.

The stator coil comprises multiple triangular turns of magnet wires ortapes. As the magnet circle turns, triangular coil overlaps with nomagnets, magnets of north polarity, or magnets of south polarity.

The magnets in FIG. 4a are of radius r. The center of the magnets is atdistance 6 r from the center of the circle. The three triangles arewounded on an outside circle of radius 8 r. As seen in the figure, theupright triangle is bounded by all 6 magnets. There is no net magneticflux inside the triangle.

When the rotor has turned clockwise by 30°, the triangle containsentirely the magnetic flux of magnets of the same polarity (north in thefigure). When the rotor turns another 30°, net magnetic flux is zeroagain. When the rotor turns yet another 30°, the triangle containsentirely the magnet flux of magnets of opposite polarity (south in thefigure). Upon completion of turning a total of 4×30°=120°, the trianglecontains again zero net flux. Magnetic flux varies as a sinusoid threecycles per 360° turn.

By Faraday's law of induction, electromotive force (EMF) induced in thetriangular solenoid of N turns is

${{v(t)} = {{- N}\frac{d\; \Phi}{dt}}},$

the rate of change of magnet flux Φ over time t. Flux Φ in each trianglehas peak value Φ_(max)=3BA for 3 magnets of magnetic field strength Bover their top of area. Induced EMF for rotational frequency f isν(t)=3NBA×2π×3f×cos(2π×3ft)=18πfNBAcos6πft.

If we use three triangles rotated by 40° relative to each other, wegenerate three-phase AC with a common neutral. The three triangles forma nine-point star as shown in the figure.

This AC generator can be used as an electric motor. By Ampere force lawdF=i×dl×B, a force vector dF is the vector product of current vector iwith length vector dl and magnetic field B. EMF power dissipated isP(t)=ν(t)i(t). EMF is converted into mechanical force.

Rotational speed of rotor depends on the balance of force between EMFand mechanical load. Without mechanical load, terminal velocity of rotoris determined by voltage amplitude ν(t). Voltage ν(t) and current i(t)are 90° of out phase with no net electrical power dissipated over time.

As we increase mechanical load, rotor velocity decreases. Induced EMFdrops. However, phase difference between current and voltage changes,resulting in dissipation of EMF to generate motion.

Thus the speed of motor is determined by voltage and torque force isdetermined by current. For AC motor, an electric speed controller (ESC)is required to control voltage and current. An ESC controls frequencyand therefore rotational speed by digital pulse width modulation method.

Since motion between triangle and circle is relative, the triangle roleas stater and the circle role as rotor can be exchanged. We can fix themagnetic circle as stator and rotate the triangle as rotor.

The motor of FIG. 4a can be modified as an induction motor as shown inFIG. 4 b. Instead of the rotor of magnets with alternating polarity, acircular conductor disk is used to generate the magnetic field ofalternating polarity. As a motor, the polyphase AC generates a rotatingpattern of alternating polarity magnetic field. By Lenz's law, thisrotating magnetic field Induces reactionary electric current in such away to oppose the magnetic field generated by the inducing current inthe polygon windings. Motion is generated during to Lenz's law inopposition to the inducing current.

To operate this polyphase AC induction motor as an AC inductiongenerator, the generator needs to be primed for motion first. Theinitial motion induces a magnetic field in the circular conductor disk.

FIG. 4c shows another embodiment of a polygon AC generator. The rotorcomprises 4 magnets of alternating parity. Each magnet has radius r.Opposite magnets of the same polarity are separated by acenter-to-center distance of 4r. Each solenoid is rectangular withdimension 2r×6r.

As the rotor rotates, each rectangle may include magnetic flux of bothnorth poles, no net flux, or flux of both south poles. Each completerotation generates two AC cycles, instead of three AC cycles for thegenerator of FIG. 4 a. Used as an AC motor, motor speed is higher. Whendriven by 60 Hertz AC, the motor of FIG. 4a rotates at 1200 rpm, whilethe motor of FIG. 4c rotates at a higher 1800 rpm.

A transducer of AC frequency and voltage is shown in FIG. 4 d. Thetransducer comprises a tandem of motor-generator of different number andkind of polygons for the motor versus the generator. As shown, the motoruses two rectangular windings such as that in FIG. 4 c, while thegenerator uses six triangular windings such as that in FIG. 4 a. ACfrequency from generator is 3 times higher than the AC frequency drivingthe motor. AC voltage depends on the ratio of turns for generator versusmotor.

No rotor is needed for the motor or generator in FIG. 4 d. The 2rectangular winding produces the magnetic field to induce voltage in the6 triangular winding. This frequency and voltage transducer is similarto voltage transformer with no moving part. Frequency transduction isfacilitated by geometry.

First Application of Tapering Spiral Turbine: A Gas Turbine withElectric Generator

Our heat turbine uses the Brayton thermodynamic cycle to convert heat towork. Pressure versus volume graph of the Brayton cycle is shown in thebottom of FIG. 2. Brayton cycle comprises four phases: adiabatic andisentropic compression of air 1→2, isobaric heat addition and expansionof gas 2→3, adiabatic and isentropic expansion of gas 1→2, and isobariccooling of the gas post turbine 4→1.

Brayton cycle heat engine efficiency is analyzed as follows. Considertemperature T and pressure p of the gas throughout the Brayton cycle.Adiabatic compression of gas (1→2) maintains constant pV^(γ) andTV^(γ−1). Adiabatic coefficient is γ=1.4 for diatomic gases. Let usassume air and fuel to be at 1 bar pressure and 300K (27° C.)temperature. Adiabatic compression of volume by a factor of 8 increasespressure to 18.38 bars and temperature to 689.2K (343.3° C.).

When fuel-air mixture is combusted under constant pressure (2→3), heatof combustion increases the volume of the combusted mixture, giving outwork as volume expands. After isobaric expansion, combusted air expandsfurther as pressure drops towards spiral exit (3→4). Work is furthergiven out by the gas expanding adiabatically inside the spiral. Exhaustgas cools externally (4→1).

Work W is given by the area in the pressure versus volume plot for theBrayton cycle. For adiabatic expansion, pV^(γ) is constant. PressureP_(L) and P_(H) are low and high pressure before and after thecompressor. Volume V_(L) and V_(H) are low and high pressure volumesbefore and after the compressor. Work done by Brayton cycle is

$W = {{\int_{p_{L}}^{p_{H}}{Vdp}} = {{C{\int_{p_{L}}^{p_{H}}{p^{- \frac{1}{\gamma}}\ {dp}}}} = {C^{\prime}\left( {p_{H}^{\frac{\gamma - 1}{\gamma}} - p_{L}^{\frac{\gamma - 1}{\gamma}}} \right)}}}$

The constants C, C′ depend on initial conditions of gas volumes.Renormalizing by the heat of combustion Q for each cycle, the efficiencyof this Brayton cycle heat engine is

$ɛ = {\frac{W}{Q} = {{1 - \left( \frac{p_{L}}{p_{H}} \right)^{\frac{\gamma - 1}{\gamma}}} = {{1 - \left( \frac{V_{H}}{V_{L}} \right)^{\gamma - 1}} = {1 - \frac{T_{L}}{T_{H}}}}}}$

Brayton cycle has constant pressure (isobaric) at two steps of the cyclewith pressure P_(L) and P_(H). Efficiency depends on the pressure ratio

$\frac{p_{L}}{p_{H}}$

or the compression ratio

$\frac{V_{H}}{V_{L}}.$

Carnot neat engine efficiency is given by

${ɛ = {1 - \frac{T_{L}}{T_{H}}}},$

which depends on the low versus high temperature ratio

$\frac{T_{L}}{T_{H}}.$

If we assume a volume compression of 8 by the compressor, pressure isincreased by 18.38 times according to a constant pV^(γ). Brayton cycleefficiency is

$ɛ = {{1 - \left( \frac{p_{L}}{p_{H}} \right)^{\frac{\gamma - 1}{\gamma}}} = {{1 - \left( \frac{p_{L}}{p_{H}} \right)^{\frac{2}{7}}} = {{1 - \left( \frac{1}{18.38} \right)^{\frac{2}{7}}} = {{1 - 0.435} = 0.565}}}}$

An implementation of our heat engine is shown in FIG. 5. The bottom ofthe heat engine is a compressor cylinder. An alternative compressor thatmay be used is the Archimedes scroll compressor shown in FIG. 9. The topis an expander cone which has a constant width spiral with taperingdepth. Compressed air passes from the top center of the compressor tothe bottom center of the expander. Fuel flows through a small tube frombottom center of the compressor to ignite in the center combustionchamber of the expander. Pressure force of expanding air post combustionturns the single compressor-expander assembly, providing motive force.Electricity is generated through the homopolar generator at the bottomof the assembly.

Second Application of Tapering Spiral Turbine: Motor Driven HeatPump/Dehumidifier

Heat pumps and refrigerators often use refrigerants such ashydrofluorocarbon (HFC). Compressing HFC gas pumps heat into thepressurized HFC which liquefies when cooled. Evaporation of liquid HFCunder reduced pressure removes heat from the environment. Thisliquefaction-evaporation cycle constitutes the Rankine cycle heat pumpprocess. However, refrigerants such as HFC if released into theatmosphere are potent global warming gas. HFC traps more than 1000 timesthe heat than carbon dioxide. HFC is scheduled for rapid replacementaccording to a recent Kigali Agreement.

Airplanes use an alternative air conditioning method that uses insteadthe Drayton cycle heat pump process. Air is bled from the compressor ofthe jet engine. A mild reduction of air pressure rapidly cools the bledair. Chilled air from cabin air vent is often misty. The mist chills airfurther with as the mist evaporates. Moist air when compressed producesfogging and misting. If we cools compressed moist air, we can removehumidity in air as well as produce water for consumption. Condensingmoisture in air also drives out the heat of evaporation of water fromair. Thus more heat removal is achieved.

This observation inspired the use of the Hui spiral compressor toproduce chill and water condensate. We explain here the thermodynamicadvantages. We introduce here a new thermodynamic heat pump processwhich we name as the Hui cycle as shown at the bottom of FIG. 3. The Huicycle merges two thermodynamic cycles: the Carnot cycle with isothermaland adiabatic phases and the Brayton cycle with isobaric and adiabaticphases. We replace the adiabatic processes of the Brayton cycle byisothermal processes. Isothermal compression reduces the amount of workneeded. Isothermal expansion increases work produced using ambient heatfrom the environment.

The Hui cycle requires compressors and expanders with built-in heatexchangers. Heat exchange can be achieved by ambient air flowing betweenspiral channels. The phases of the Hui cycle is shown in FIG. 3. Thereare three temperatures: ambient temperature T_(a), high temperatureT_(H) at which heat is extracted, and low temperature T_(L) at whichchill is produced.

Phase 1→2 is the isothermal compression phase of gas at T_(H), requiringcompression work W_(c)=nRT_(H)lnp_(H)/p_(L) in which p_(H), p_(L) arethe high and low pressures of the isobaric phases. This work is changedentirely into heat of compression Q_(c) dissipated without increasingthe temperature of the gas.

Phase 2→2a is the isobaric cooling of the gas from high T_(H) to ambientT_(a). Phase 2a→3 is the further isobaric cooling of the gas fromambient T_(a) to low T_(L).

Phase 3→4 is the isothermal expansion phase of the gas at the low T_(L),producing work of expansion W_(e) by the heat absorbed Q_(e), withQ_(e)=W_(e)=nRT_(L)lnp_(H)/p_(L).

Phase 4→4b is the isobaric heating of the gas from low T_(L) to ambientT_(a). Phase 4b→1 is the further isobaric heating of gas from ambientT_(a) to high T_(H).

We use counter flow heat exchangers to reuse heat. For Phase 2→2a, heatgiven out is exactly absorbed by Phase 4b→1. For Phase 2a→3, heat givenout is exactly absorbed by Phase 4→4b.

We attribute performance of heating and chilling as follows. Thecoefficient of performance of heating COP_(h) is the heat produced Q_(h)divided by the net work done W_(net)=W_(c)−W_(e). Thus

${COP}_{h} = {\frac{{nRT}_{H}\ln \; {p_{H}/p_{L}}}{{{nRT}_{H}\ln \; {p_{H}/p_{L}}} - {{nRT}_{L}\ln \; {p_{H}/p_{L}}}} = \frac{T_{H}}{T_{H} - T_{L}}}$

The coefficient of performance of cooling COP_(c) is the chill producedby isothermal expansion Q_(e) divided by the net work doneW_(net)=W_(c)−W_(e). Thus

${COP}_{c} = {\frac{{nRT}_{L}\ln \; {p_{H}/p_{L}}}{{{nRT}_{H}\ln \; {p_{H}/p_{L}}} - {{nRT}_{L}\ln \; {p_{H}/p_{L}}}} = \frac{T_{L}}{T_{H} - T_{L}}}$

Consider the heating of water from T_(a)=27° C. (300K) to T_(H)=77° C.(350K) and for cooling of air from T_(a)=27° C. (300K) to 7° C. (280K).We have

${COP}_{h} = {\frac{350}{350 - 280} = {{5\mspace{14mu} {and}\mspace{14mu} {COP}_{c}} = {\frac{280}{350 - 280} = 4.}}}$

Traditional chilling compresses refrigerant such as CFC which depletesozone, or HFC which traps heat. We should compress air directly insteadof compressing a refrigerant, The Hui cycle can achieve ideal heat pumpefficiency. Work is recovered from the expanding gas, in contrast,evaporating refrigerant produces no work. Without efficient aircompression with high compression ratio, liquefaction of refrigerant ispreferred. Substantial research is aimed at finding effectiverefrigerants that do not harm the environment. With compact spiralturbines, we can compress air effectively. We can therefore avoid theuse of refrigerants.

Better yet, compressing humid air condenses moisture in air upon removalof heat of compression. The heat of condensation is dispersed.Traditional air conditioning requires the use of chill produced by theevaporation of refrigerant gas to remove humidity and its heat ofcondensation. Dehumidifying air increases the work load of the airconditioner for the same drop of air temperature.

The condenser of traditional air conditioner is located outside thebuilding, condensing humidity that often drips down on people. For ourproposed air conditioner, we contain the condensing moisture inside anenclosed condenser. The collected moisture can be emptied by a tube orcollected for human and plant consumption.

Evaporating water exerts a vapor pressure that depends only ontemperature. That vapor pressure is part of the pressure exerted byhumid air. Each component gas of air exerts its own vapor pressure. Aircomponents include oxygen (19% by volume), nitrogen (80%), argon (1%),and water (percentage depending on humidity level). Atmospheric pressureis the sum of the vapor pressure of various air components. Total vaporpressure is around 1 bar at sea level.

Humidity of air is defined as water content in air divided by watercontent in 100% humid air. Dew point is defined as the temperature whenthat air is cooled to the point that water starts to condense in 100%humid air. Dew point and air temperature are the same with 100%humidity. Take for example 100% humid air at 25° C. and 14° C., whichcontains respectively 2 grams of water and 1 gram of water for 100 gramof air. Thus the dew point of 50% humid air at 25° C. is 14° C.

What happens to air moisture if we double the pressure of 100% humid airat 25° C.?Initially, vapor pressure of all air components doubles. Humidair, which is heated up by compression, is cooled back down to 25° C.Since water vapor pressure depends only on temperature, increased watervapor pressure due to compression causes water to condense. Half of thewater vapor of air would have to condense out to restore to the samevapor pressure of water at 25° C.

For high humidity air, most moisture in air condenses out if wecompresses air volume by a factor of 2 to 4. That condensation releasesa significant amount of heat of condensation. Consider increasingpressure by a factor of 2 for 80% humid air at 25° C. That air has 1.6grams of water per 100 grams of humid air. increasing pressure andsubsequent cooling of humid air would force 0.6 grams of water out. Atmore than 2200 joules of heat of evaporation per gram of waterevaporated, pressure would drive out 1321.2 joules of energy for 0.6grams moisture condensed.

This heat is significant compared the cooling of air. Consider thelatent heat of cooling 100 grams of air by 20° C. The heat that requireschilling removal is

${\Delta \; H} = {{{anR}\; \Delta \; T} = {{2.5 \times \frac{100\mspace{14mu} g}{28\mspace{14mu} g} \times 8.3 \times 20} = {1482\mspace{14mu} {J.}}}}$

Quadrupling pressure of 80% humid air at 25° C. would force out 1.2grams of water vapor with heat of condensation of 1.2 g×2200 J/g=2640 J,which is more than the heat removed for cooling air by 20° C. Waterremoved from air produces water for human or plant consumption.

FIG. 6 shows the heat pump for generation of hot water, chilled air, andcondensed water. A top compressor driven by our motor compresses airfrom the bottom center of the compressor into a heat exchanging tube.The tube goes through the center of a water tank, giving its heat of aircompression and water condensation to heat up water in the tank.Condensed water and cooled compressed air are collected at the bottomtank. Compressed air drives the expander at the top, giving chilled airfor space cooling. Compressed air can also be distributed over nylontubes to expander in room for chilling as well as generating work andelectricity for lighting and consumption by appliances.

Third Application of Tapering Spiral Turbine: Solar Water Desalination

We can use the spiral compressor for solar desalination of water.Electricity for driving the compressor can be produced by solar thermalor photovoltaic power. Solar energy can be concentrated and collected asheat to boil sea water at reduced air pressure. Our spiral compressorcan be used to condense steam from solar evaporated salty water. Theheat of condensation can be used to evaporate more salty water. Thus ahigh efficiency of water desalination can be achieved.

Solar desalination was inspired while I heard a loud hissing sound andsaw steam coming out of a solar water heater in Tibet of China. The lowair pressure of Tibet makes water boils at a lower temperature than 100°C. Water boils at 80° C. when atmospheric pressure is halved.

We can recreate this low pressure environment at the head of a tailwater column. Water boils at 80° C. on top of a 5 meter water columnwhere pressure is halved. A 10 meter water column has zero pressure atthe top where water would evaporate profusely. Resulting vapor pressurecauses the water column to drop. We would need a pump to remove vapor inorder to create a near vacuum at the top.

FIG. 7 shows a novel solar water desalination device. For conventionalsolar water heater, solar heat is trapped to heat water in a glass tube.That glass tube is contained in another vacuumed glass tube. The outerglass tube has a reflective half surface that reflects sunlight onto theinner water heating tube. Similar to solar water heater, we use a muchlarger reflector of light. The reflector is shaped like a conic surfaceas shown in FIG. 8 to concentrate sunlight onto a vertically placed tubeof water. The reflector tracks the sun in the azimuth position α. A sundue North has α=0°. The reflector also tracks the sun in the altitude orelevation, defined as the angle β sunlight makes with the horizon. Adirectly overhead sun at zenith has β=90°. A sun on the horizon hasβ=0°.

FIG. 8 shows a conic reflector, which is part of the curvilinear surfaceof a cone. We call the center line of the conic surface the apex line.The apex line should follow the azimuth location of the sun. To trackthe sun in its altitude, the apex line tilts with angle δ from zenithsuch that reflected light shines horizontally on the vertical saltywater column.

A horizontal cross section of the conic surface is a parabola with focuson the vertical z-axis. Consider a directly overhead sun at the zenithwith β=90°. If the apex line is tilted with δ=45°, overhead sunlight isreflected horizontally onto the column of salty water. The reflector isconic in the sense that the cone is formed by rays from the origin(0,0,0).

Consider an elevation of δ=45° for the conic surface as shown in FIG. 8.Let the tip of the cone be located at the origin (x,y,z)=(0,0,0). Thecolumn of salty water is centered on the z-axis. The parabolic crosssection at level z has apex minimum located at (x,y,z)=(0,z,z). Light isfocused onto (x,y,z)=(0,0,z) with focal length p=z if the sun isdirectly overhead with β=90° as shown in FIG. 8. For a given verticallevel z, the parabola at level z is x²=4p(z)(y−p(z)), in which (p(z) isthe focal length of the parabola at level z.

Consider the more general case of β>0. We want to reflect sunlight sothat it hits the vertical column horizontally. The resulting tilt of theapex line is

$\delta = {\frac{\beta}{2}.}$

For the sun at zenith β=90°, tilt is δ=45°. The apex line is theequation y=z tan δ on the y-z plane. The conic surface is given by theequation x²=4z tan δ (y-z tan δ) as shown in FIG. 8. The conic surfaceis curvilinear in the sense that a flat sheet of reflective material canbe put on the surface of a cone. The focal length at level z is z tan δ.

While it is important for the reflector to track the sun well in theazimuth position, it is less important to be able to track the sunexactly in the altitude. The resulting focal line remains on the z-axis,although the line may be shifted up or down on that axis according tothe altitude of the sun. Thus it may be sufficient to have prearrangedtilting of δ for the reflector, such as δ=15°, 30°, and 45° for altitudeof the sun β=30°, 60°, and 90° respectively.

Reduced pressure at the head of water makes water boil at lowertemperature. Water boils when vapor pressure of water is equal to theambient pressure. Vapor pressure depends only on temperature. As shownin FIG. 7, the key step for water desalination is to compress lowpressure water vapor to condense at higher pressure. A spiral compressoris placed above the head of water to remove vapor.

The compressed and heated water vapor emerges from the center of thespiral compressor into a long thin tube down the center of the watercolumn. Water condenses as water vapor yields its heat in exchange withthe surrounding boiling water. Condensed water is collected in theclosed vessel at the bottom of the column as shown in FIG. 7. Freshwater can be pumped out of the condensation chamber.

As water vapor condenses, it yields significant amount of heat ofcondensation. Capturing this heat of condensation significantly enhancesthe efficiency of water distillation.

As water head, evaporation concentrates saltiness. This heavy and hotbrine solution is discharged after yielding its heat to incoming saltywater through a counter flow heat exchanger.

Efficiency of desalination has thermodynamic limits. More heat isrequired to evaporate salty water than heat released by condensingsteam. Also, compression of steam by the spiral turbine requires workthat is changed into heat of compression. However, extra energy requiredcan be abundantly supplied by solar thermal and photovoltaic power. Heatis lost by convection on the outside of the salty water column. Withgood insulation and heat exchange, we expect high efficiency.

Electricity for operating the compressor can be supplied solarphotovoltaic cells. Electricity is used to compress low pressure watervapor. Motion energy is converted into heat of compression. Both heat ofcompression and condensation are used for more evaporation of saltywater.

The predominant way of thermal desalination employs multistage flashdistillation. Seawater is heated by fossil fueled power plants. Hotseawater is flashed into successive stages of evaporation chambers withprogressively reduced pressure. We use a spiral compressor instead ofstaging.

Drinking salty water has become a health problem in the Indiansubcontinent. Pacific islanders can also draw on solar desalination fordrinking and cleaning purposes. We hope the new method of solardesalination can be of vital help to coastal people without usingpolluting and expensive fossil fuel.

Detailed Description of Tapering Exponential Spiral Expander andCompressor

FIG. 1 shows the tapering exponential spiral (top) and its embodimentsas an expander (bottom left) and compressor (bottom right).

The spiral has outer wall 001 that comprises a radius that has made turnangle θ 002. The radius is of length indicated by 003.

The spiral has inner wall 004 of lesser length than the outer wall. Theradial distance between the inner and outer wall decreases exponentiallyas the turn angle with width indicated by 005.

The beginning of the spiral channel 006 is wider than the end of thespiral channel 007. Gas flow depends on spiral spin direction. If thespiral is turning in a clockwise direction, gas flows from inside tooutside by centrifugal force. The outflowing gas expands, if the spiralis turning in an anticlockwise direction, gas flows from outside toinside by centripetal force, thereby compressing the inflowing gas.

An embodiment of a tapering exponential spiral expander 101 is shown inthe bottom left disk of FIG. 1, comprising a plurality of 4 spiralchannels 102, 103, 104, 105, each of which spirals outward in ananticlockwise direction. This plurality allows more gas flow in a disk,thus enhancing the power of the turbine. The spiral turbine disk 101turns in a clockwise direction as indicated by 110 in reaction to gasflowing anticlockwise in these spiral channels.

For spiral channel 102, gas flows from the spiral inlet 108 for 1.5turns before reaching the spiral outlet 107. Anticlockwise flowing gaspresses against the outer spiral wall of spiral channel 102. For spiralchannel 105, gas flow direction is indicated by the arrow from the inlet108 and the arrow at the outlet 109. These two arrows indicate ananticlockwise flow of 1.5 turns.

For spiral channel 102, the outer wall of the spiral compresses twoparts. The first part 106 has a faster exponentially growing radius for

${- \frac{\pi}{2}} \leq \theta \leq 0.$

There is no inside wall for that range of θ: gas comes into the spiral102 through the gas entry center hole 108. The inner wall of the spiral102 is the outer wall of spiral 103 for the range

$0 \leq \theta \leq {\frac{\pi}{2}.}$

The inner wall 107 of the spiral 102 for the range

$\frac{\pi}{2} \leq \theta \leq \frac{5\; \pi}{2}$

is the outer wall of spiral 102 less a constant spiral width w for thatrange of θ.

While the radius r is exponentially expanding in θ, the spiral bore canbe tapered by depth d of the spiral that is decreasing exponentially inθ, which is equivalent to a linearly decreasing d versus radius r. Thuswhen viewed sideway, the disk shaped expander resembles a cone 513 asshown in FIG. 5.

The same expander 101 when spun in the opposite anticlockwise directioncan become a gas compressor which compresses gas from outside inwardstowards the center of the spiral disk.

The bottom right of FIG. 1 shows a compressor 111 with 4 exponentialspirals 112, 113, 114, 115 going from inside to outside in a clockwisedirection. This plurality allows more gas flow in a disk. The spiralturbine disk 111 turns in a anticlockwise direction as indicated by 120.The motive force for this anticlockwise spinning can be provided by aspiral expander 101 spinning in the same clockwise direction. The spiralexpander could be stacked on top of the spiral compressor as a singlegas turbine as shown in FIG. 5, with the coaxial expander-compressorspinning in the same clockwise direction.

The spiral compressor 111 can be driven by a motor instead. Forcompressive condensation of low pressure steam from evaporated saltywater in FIG. 7, a motor drives the compressor.

For spiral channel 112, gas flows from the outside spiral inlet 112 for1.5 turns before reaching the spiral outlet 118 at the center of thespiral disk 111. Anticlockwise flowing gas is pressed by the outerspiral wall of spiral channel 112, increasing gas pressure as it flowstoward the center of the spiral disk. For spiral channel 115, gas flowdirection is indicated by the arrow from the inlet 119 and the arrow atthe outlet 118. These two arrows indicate an anticlockwise flow of 1.5turns.

The depth of the spiral channels can be tapered from center to outside.Gas flows from outside to inside slows down due to the expansion ofspiral depth from outside to the center.

Gas can be allowed to flow in between spirals, driven by the rotarymotion of the turbine disk. Gas flowing in between spirals can exchangeheat with gas flow inside spirals. For gas compression, compressed gasinside spiral may be cooled by gas flowing in between spirals, achievingmore isothermal than adiabatic compression. For gas expansion, expandinggas inside spiral may be heated up by gas flowing in between spiral,giving more motive force for gas expansion.

These spiral compressors and expanders may operate in stages. Acompressor 111 may be stacked coaxially with an expander 101, with gasflowing through a shared center for gas to flow from the center 118 ofcompressor 111 to center 108 of expander 101. Compressors can also becoaxially stacked for higher compression ratio, with gas channelsflowing from center 118 to inlet 112 by radial conduit. Expanders canalso be coaxially stacked with similar radial channels from outlets toinlets. Gas compression can also be enhanced utilizing the channels inbetween spirals, using these channels as centrifugal or centripetal gascompression.

Detailed Description of Electric Generator

FIG. 4a shows an implementation of a three-phase AC electric generator401 with three triangular stator induction coils 402, 403, 404 foroutput phases 405, 406, 407 and a circular magnetic rotor 408 ofpermanent magnets 409, 410, 411, 412, 413, 414 alternating polaritieswith marked north (N) and south (S) poles. As motion is relative, theinductor coil may rotate in a static magnetic circle instead.

The magnets are equally spaced on a circle of radius centered at 415,which is also the axis of rotation. These magnets are axiallymagnetized. Each magnet is placed inside a socket in the rotor. Thebottom of these magnets are placed on plate 416 of high magneticsusceptibility for magnetic flux to flow among alternating poles on theplate. This provides easy permeation of magnetic field.

The other ends of these magnets are air gaps such as one labeled as 417.Above the air gaps is another plate 418 of high magnetic susceptibility.This plate allows easy permeation of magnetic field among the poles. Theplates 416, 418 may be connected by a hollow cylinder 419.

The triangular stator coil 402 has three sides 420, 421, 422 and threeincluded angles 423, 424, 425. The side 420 lies just above the magnetpair 412, 413. Similarly, the side 421 lies just inside the magnet pair410, 411, and the side 422 lies just inside the magnet pair 409, 414.The triangular stator coils 403, 404 are similarly bounded by the magnetpairs.

These three coils formed a nine-point star with all corners of thesolenoids affixed on the stator case 426. The 3 triangular coils areshifted relative to each other by 120°, ⅓ of the 360° turn. The coil 402has net zero magnetic flux. The coil 403 includes about ⅔ of southwardmagnetic flux. The coil 404 includes about ⅔ of northward magnetic flux.

As the circle of magnet turns, magnetic flux changes inside each coil.Consider turning coil 402 in steps of anticlockwise turns each of 30°.The corner 425 moves to 427, containing all magnetic flux from the northpole of magnet 409. The corner 423 moves to 428, containing all magneticflux from the north pole of magnet 413. The corner 424 moves to 429,containing all magnetic flux from the north pole of magnet 411. Coil 402has maximum northward magnetic flux.

If the triangular coil 402 is turned anticlockwise by another 30°relative to the circle of magnets, the corners 430, 431, 432 contains nomagnetic pole, making net magnetic flux zero again.

If the coil 402 is turned anticlockwise by another 30°, the corners 433,434, 435 contains the south magnetic poles 414, 412, 410 respectively.Coil 402 has maximum southward magnetic flux.

If the coil 402 makes yet another anticlockwise turn by 30% the cornersare located now at 423, 424, 425 back to the initial positions of thecoil with zero net magnetic flux inside the triangle.

The coil made four 30° turns for a total of 120°. EMF output 405completed phase change of 360°. If the rotor turns at a frequency of fHertz, each phase has a frequency of 3f Hertz .

The two other coils work similarly. Since the three coils are offsetfrom each other by 120°, the power outputs are also offset from eachother 120°. Three output loads 436, 437, 438 consume the electricalpower produced. As load increases, rotation speed slows, voltage drops,and current increases.

The same apparatus for electricity generation can operate as an electricmotor to convert electricity to motion. Output load 436, 437, 438 arenow the output of an electronic speed controller ESC. Controlledfrequency, voltage, and current create a torque on the rotor to drive amechanical load.

This polygon electric motor can be modified as a polygon induction motoras shown in FIG. 4 b. The polygon induction motor has a rotor centeredaround the axle 439. The rotor uses a circular conductor disk 440 forthe rotor instead of the rotor of magnets of alternating polarity.Lenz's law states that magnetic action and reaction are equal andopposite. The polygon windings induce currents in the circular conductordisk 440. Motion results from the opposing magnetic fields in the statorand rotor.

FIG. 4 b, a single-phase AC power source 441 induces a changing magneticfield in the triangular coil 442 mounted on stator 443. The coil 442induces currents in the circular disk 440, producing rotating magneticfields of alternating polarity. To prime the rotation in a desireddirection, a capacitor 444 is used to make current to lead the voltage.The leading current 445 then drives another triangular winding 446. Thisinduction motor is also a generator, requiring a priming current tostart the generator.

Another AC generator is shown in FIG. 4 c. The rotor 447 comprises 4magnets 448, 449, 450, 451. The stator 452 comprises 3 rectangularsolenoid coils 453, 454, 455 to generate three phases of electricity456, 457, 458 with a common neutral 459. Motion by axle 460 is convertedinto electricity.

A motor-generator pair of FIG. 4d can be used to transduced AC frequencyand voltage of a power source 461. The pair shares an inductive rotorplate 462. Beneath the plate is the motor stator with 2 rectangularwindings 463, 464, connected by capacitor 465 to give current in 464 a90° phase lead. The stator windings drive the rotor 462. The inducedcurrent in the rotor in turn induces current in 6 triangular windings468, 467, 468, 469, 470, 471 above 462. Winding pair 466, 469 isconnected in series by 472, with one neutral end 473 and the other endyields an AC phase 474. Pair 467, 470 connected by 475 yields another ACphase 476. Pair 468, 471 connected by 477 yields the third AC phase 478.

The rotor plate 462 can be superfluous, as the single phase AC in therectangular winding can induce directly three phase AC in the triangularwinding. The resulting transducer without rotor is static.

Detailed Description of Integrated heat Turbine and Generator

FIG. 5 shows the cross section views of heat turbine and generator. Theheat turbine comprises a compressor 501, the heat chamber 502, and theexpander 503, with the horizontal cross section view shown as two4-spiral disks on the top and bottom of FIG. 5.

Four compressor spiral channels 504, 505, 506, 507 turn to compress airfrom outside in. Compressed air then passes from the center of thecompressor 501 into the heat chamber 502. As the compressor turns in onedirection (shown clockwise in the figure), gas is compressed by flowingin the opposite direction in the compressor spiral channels(anti-clockwise in the figure).

For heat generation by gas combustion, combustible gas enters the heatchamber 502 through fuel nozzle 508 where the fuel-air mixture ignites.

For heat generation by concentrated solar thermal power, sunlight isfocused on the top center of the expander 513, possibly with a glass topto allow focused sunlight to enter the chamber.

As a single turbine turning in one direction, the compressor 501 andexpander 503 turns in the same clockwise direction. Gas expands in thefour expander channels 509, 510, 511, 512. Gas rotates in these channelsin opposite direction (anti-clockwise) of the rotation of the turbine.Pressure of gas turns the turbine clockwise. Pressure expended gas exitsat the periphery of the expander.

The expander spirals are tapering by means of decreasing depths, from alarger depth of 513 near the center to a smaller depth 514 near theexit. This tapering allows slow release of pressure in spirals.

The compressor spirals may be tapered to induce a higher compressionratio. We may employ a stack of multiple compressors in stages, actingalternately as centrifugal and centripetal compressors,

In an alternative embodiment of the compressor, we can use a scrollcompressor comprising two Archimedes spirals shown in FIG. 9 instead ofthe tapering spiral compressor. Scroll compressor allows for a high gascompression ratio due to closure of gas between the two scrollingArchimedes spirals. The scrolling however is abrasive for the contactpoints of the scrolling spirals.

The turbine spins around two ends 515, 516 on the axis of spinning fixedon turbine casing. We may use ball bearings, air bearings, or magneticbearings for smooth spinning.

The electric generator 517 is shown on the periphery of theturbine-generator. We place magnets 518 on the rim of the rotor diskwith opposite poles on the top and bottom of the disk as shown.

We use two toroidal solenoids 519, 520 on top and bottom of the magnets.These two solenoids can be connected in series to double voltage output.These two solenoids can act as magnetic bearing for the turbine. Thepermanent magnet 518 is levitated by magnetic forces from the solenoids519, 520.

The two ends 521, 522 form the terminals of the DC generator. Anexternal load 523 consumes the electricity generated. A load controllerin may be used to control the spin velocity of the turbine. A highvoltage increases spin velocity, low external load resistance increasescurrent flow. High current flow exerts a strong torque resistance to thework provided by the heat turbine.

The heat turbine may exert work directly on an external mechanical loadsuch as gear box of an automobile or the turboprop of an aircraft.Electricity generated can be stored via chemical batteries orsupercapacitors. DC electricity generated is stored without DC to ACinversion. The DC electricity stored can be retrieved as DC to drive anelectric motor. The electric motor is the same electric generator of thecombined compressor-expander-generator-motor shown in FIG 5. We may notneed another motor.

Detailed Description of Air Conditioner and Dehumidifier

An implementation of an air conditioner and dehumidifier is shown inFIG. 6. The top of the FIG. indicates a combined single rotor ofcompressor 601 and expander 602.

We divert compressed air downward to heat exchanger 603 that yields gasheat to a water heating tank 604. Cooling of compressed air yields itsmoisture condensing in chamber 605 and collected through 618. Cold waterenters at 616 to be heated in the water tank 604. Hot water is extractedat 617.

Cool compressed air is then further cooled by ambient air through aconduit 606 to the expander 602. Pressure expended air from the expander602 is ducted through vent 607. The expander also serves as an airblower for delivery of cooled and dried air to rooms in a building.

The compressor is powered by motor 608 identical in structure to thegenerator for the heat turbine. The rotor magnet 609 is a ring withmagnetic axis aligned with the rotor axis of rotation. The stator coils610, 611 are powered by DC power source 612.

A motor control 613 controls motor voltage and current. Voltage controlsspinning velocity. The compressor motor is ramped up gradually to therequired speed for compression. Current controls torque force requiredfor the compression. The compressor is hinged with bearing at 614, 615.

An alternative implementation decouples the compressor 601 from theexpander. Compressed air could be delivered by thin nylon tubes toindividual rooms. An expander is located in each room, delivering chilland possibly electricity generated by the spinning expander.

This alternative could be used for villages with centralized compressorand electricity generator. Power for the compressor could be derivedfrom solar panels or from our heat turbine driven by solar heat or gascombustion. Compressed air could also be stored in large volume forevening usage. We deliver compressed air to huts by thin nylon tubesinstead of power through metallic conductors. Compressed air provideschill and refrigeration to individual homes. The expander located ineach home could also integrated a generator to generate low voltage DCfor LED lighting, TV, and battery charging.

We describe here also a portable embodiment of the air conditioner anddehumidifier. The unit can be placed on a person's back for cooling anddehumidifying. The embodiment is similar to that of FIG. 6 without theheat exchanger 604. The top compressor-expander is placed on near thetop of the paraboloid with the top surface of the paraboloid blowingcooled air onto our back. The bottom condenser collects compressed airto he cooled, dehumidified, and returned to the expander.

Detailed Description of Solar Water Desalination

FIG. 7 shows a water desalination system that employs solar power toevaporate salty water under reduced pressure. Photovoltaic power 714 maybe used to drive the compressor 704.

The desalination system has water heating and steam condensationsubsystem similar to that for air conditioning with dehumidifying. Wecompress low pressure steam instead of humid air.

A tall water column 701 has reduced pressure at water head 702. The saltwater tank 703 may be made of strong glass, reinforced concrete, orceramic material that can withstand salt water corrosion.

Above the water head and inside the water tank 703, a compressor 704 ishinged at 712, 713 and driven by a motor 705. Compressor draws in lowpressure steam from inlets 715, compressing and heating that steam.Steam exiting 713 heats salty water in tank 703 for further evaporation.

Cooled steam condenses as water in the chamber 707, which can be drawnout through 708.

The circulation of salty water is as follows. Salty water can bepreheated before entering water chamber 703 through inlet 710.Preheating can be achieved through heat exchange with salty brine waste.We may preheat salty water in solar water heaters with vacuumed glasswater heating tubes.

A parabolic solar power collector 709 focuses solar energy onto thesalty water column 703. The geometry of the collector is shown in FIG.8. Focused sunlight heats up the salty water, which rises to the top 716and evaporates profusely with the reduced pressure at heat of water. Thewater is also heated fey the condensing steam in the heat exchanger 706.

Denser brine migrates to 717, cools because of further evaporation, andsinks to the bottom. The brine waste exits at 711. Heat exchange mayoccur between hot brine waste and incoming salty water.

To facilitate circulation from inlet 710 to outlet 711 through the toplocations 716, 717, we may partition the vertical volume of the saltwater tank into sectors. The sector boundaries can also absorb focusedsunlight should the salty water tank be made of transparent glass.

Salty water can also be heated by hot air exhaust from gas poweredturbine. This configuration could be used for purifying contaminatedwater produced by tracking at oil wells. Combined heat engine and solarwater desalination can also be a true life saver for ocean vessels andstranded islanders.

CONCLUDING REMARKS

There are three essential elements for human survival: air, water, andsunshine. From these three, perhaps with the assistance of gaseous fuelas backup, we derive all human comforts of cooling, heating, food, waterfor drinking and cleaning, and energy needed for communications,computing, and transportation. We believe the inventions described willprovide these human comforts where and when needed through the paradigmof personal energy instead of centralized generation.

Acknowledgment; Jim Hussey, Ankur Ghosh, Forest Blair, and Jerry Jin ofMonarch Power implemented and tested early versions of turbine. RonanReynolds of Monarch Power Corp 3D modeled inventions of this patent forprototyping, testing, and validating the theory presented in this patentapplication. Professors Daniel Bliss of Arizona State University, Y CChiew of Rutgers University, and Falin Chen of National TaiwanUniversity stimulated discussion of the fluid dynamics of the spiralturbine. Professor Keng Hsu of ASU 3D laser printed an early metalturbine.

1. I claim for a spiral turbine as an energy conversion device betweenheat energy and motion energy via pressure change of a gas, comprising:a plurality of coaxial disks, each of said plurality of disks having aplurality of enclosed spiral channels adapted for spiral flow of a gasbetween a center and a perimeter of each of said plurality of disks;wherein each of said spiral channels comprising: increasing radii thatincrease with the angle turned by the radii, and a bore area thatdecreases with the angle turned, such that an outer spiral channel wallhas a larger area than an inner spiral channel wall; said plurality ofenclosed spiral channels adapted to provide gas flows there within, thegas flows providing energy exchange between pressure energy of the gasacting on said inner and outer walls so as to produce a torque leveragedby the radius and the motion energy of said coaxial disks.
 2. The energyconversion device of claim 1, wherein said a bore area that decreasesmonotonically with the angle turned.
 3. The energy conversion device ofclaim 1, wherein said a bore area that decreases logarithmically withthe angle turned.
 4. The energy conversion device of claim 1, whereinsaid plurality of coaxial disks include tapering exponential spirals,and coaxial stacking of said plurality of coaxial disks is arranged instages utilizing both said tapering exponential spirals and saidplurality of enclosed spiral channels situated in between said taperingspirals exponential spirals; wherein wherein said tapering exponentialspirals and said plurality of enclosed spiral channels are connectednear a center or perimeter of said coaxial disks.
 5. I claim for anelectric machine as an energy conversion device to transform motionenergy into electrical energy; said device comprising: a plurality ofcoaxial magnetic disks, comprised of an annulus of permanent magnetswith alternating polarity oriented axially, wherein each of saidplurality of coaxial magnetic disks having a plurality of induction coildisks, said induction coil disks comprising a plurality of coaxialpolygonal conductor windings, wherein the induction coil comprising twoends, a first end comprising a phase of power generated and a second enda connection to neutral; wherein motion energy is exchanged betweenelectricity flowing in said plurality of induction coil disks and therelative rotational motion of plurality of coaxial magnetic disks andsaid induction coil disks.
 6. The energy conversion device of claim 5further comprising a polygonal induction coil, and induced multiplephase alternating electric current between the said plurality of coaxialmagnetic disks and plurality of induction coil disks, said electriccurrent inducing by an electric field to drive an electric current,wherein said electric field is induced by the relative rotational motionthat changes the amount of magnetic flux flowing from a circle ofmagnets of alternating polarity through said polygonal induction coil.7. The energy conversion device of claim 5 wherein said plurality ofcoaxial magnetic disks comprise a single circular conductor disk, saidconductor disk adapted to provide mutual induction of current betweensaid plurality of coaxial polygonal windings and said circular conductordisk to enable conversion between kinetic and electric energies.
 8. Theenergy conversion device of claim 7 wherein said plurality of polygonwindings having a different number of sides of each polygon windings,wherein said plurality of generator polygonal windings connected inseries.
 9. The energy conversion device of claim 7 further comprising: afirst set of polygonal windings of said plurality of polygonal windingsis driven by an alternating current of a voltage, a frequency, and anumber of phases to be transduced, said first set inducing directly on asecond set of polygonal windings of said plurality of polygonalwindings, said second set comprising a different number of sides andnumber of turns from the first set, wherein said first set and saidsecond set connected in series.
 10. I claim for a gas turbine as a diskshaped expander turbine powered by a pressurized gas, said turbinecomprising: a central chamber adapted to accept pressurized gas isinjected by a nozzle, whereby the gas is heated in said central chamber;a plurality of enclosed spiral channels radiating from said centralchamber, each of said plurality of enclosed spiral channels comprisingexpanding radii and tapering bore; wherein said tapering bore is adaptedto release pressure gradually through the length of the spiral and outof a perimeter of said turbine; wherein said turbine is adapted toretain pressure on a larger outer surface area than an inner surfacearea of spiral of decreasing bore area versus an increasing radius, thusallowing the gas pressure to force rotation of said turbine in theopposite direction of the gas flow.
 11. The disk shaped expander turbineof claim 10 further comprising a disk shaped compressor turbine adaptedto supply pressurized gas, said compress turbine comprising: a pluralityof disks, with each of said disk comprising: a second plurality ofenclosed spiral channels, with each spiral channel of said secondplurality comprising a decreasing radius and tapered bore adapted tocompress gas flowing from a periphery of the disk towards a center ofthe disk, such that the larger radius and surface area of an outsidewall of the tapered bore produces a larger torque force at a perimeterthe compressor turbine to compress the gas towards the center of thedisk.
 12. The disk shaped turbine of claim 10 wherein said disk shapedcompressor comprises an Archimedes scroll compressor.
 13. The diskshaped turbine of claim 10 wherein said plurality of enclosed spiralchannels comprise radii that grow exponentially as the angle turned. 14.The disk shaped expander turbine of claim 10, wherein said disk shapedturbine is mated with an electric generator and adapted to serve as arotor for said generator, said electric generator further comprising anannulus of electromagnets around said disk shaped turbine adapted toinduce electricity on stator coils that are co-axial with said diskshaped turbine.
 15. I claim a heat pump as a method of utilizingcompressed gas to drive an expander turbine to produce work and coolingof the expanded gas, said method comprising the steps of: forcing gasthrough a compressor into a spinning turbine central chamber, wherebythe spinning turbine chamber comprises: a plurality of enclosed channelsfor spiral flow of gas from the center to the perimeter of each disk;and each spiral channel comprising: increasing radii that increaselinearly or exponentially as the angle turned by gas in channel, and abore area that decreases as the angle turned by the spiral channel; suchthat gas flows with pressure that decreases gradually with angle turnedby exerting pressure force on the outer spiral channel wall, producingwork and cooling the gas as gas heat is converted into motion energy.16. The method of claim 15, further comprising the step of producingchill by expanding compressed gas in the spiral channel via a compressorheat pump for producing heated and compressed gas and subsequent coolingof the heat gas while retaining the pressure of the gas.
 17. The methodof claim 16, wherein the compressed gas is delivered by tubes from adisk shaped compressor made to rotate by an external torque, comprising:a plurality of spiral channels comprising decreasing radii and bore fromdisk perimeter towards a center chamber for compressed gas; wherein gascompressed from the outside of said compressor is forced to the insidethrough said spiral channels in reaction to compressing force of thelarger outer surface area of these spiral channels.
 18. The method ofclaim 17, wherein said step of forcing gas utilizes a motor adapted toutilize said disk compressor as a magnetic rotor of an electric motor todrive said compressor.
 19. The method of claim 17 further comprising thestep of cooling produced hot compressed air by heat exchange with acondenser that produces hot water.
 20. The method of claim 17 furthercomprising the step of producing potable water, said potable water beingderived via said gas wherein sad gas comprises humid air, and saidpotable water is extracted from moisture in said humid air aftercompression and cooling.
 21. The method of claim 17 further comprisingthe steps of: receiving air in a container from said compressor, thecontainer adapted to store air after dehumidified as cooled, pressurizedand dehumidified air; powering a disk shaped turbine via a pressurizedair supplied from the container, wherein the disk shaped turbineincludes: a central chamber into which the pressurized gas is injectedby male nozzles and the gas is heated in the chamber by means of fuelcombustion or concentrated solar energy; a plurality of spiral channelsradiating from the central chamber, the plurality of spirals comprisingexpanding radii and tapering bore; wherein the tapering bore adapted torelease pressure gradually through the length of the spiral and out of aperimeter of said turbine; wherein the turbine is adapted to retainpressure to act on the perimeter, the perimeter having a larger outersurface area than an inner surface area of the tapering bore, thusallowing the gas pressure to rotate the turbine In the oppositedirection of the gas flow.
 22. The method of claim 17 further comprisingthe step of cooling the air by injecting water for evaporation.
 23. Iclaim a water purification device comprising: a water column withreduced head pressure to reduce the boiling point of water to bepurified; a compressor at the head of the column to reduce head pressureand to compress low pressure steam evaporating from head of column; aheat source coupled to said water column; a heat exchanger inside saidwater column for condensing steam to exchange steam heat of compressionand heat of condensation to provide for further evaporation of water inthe water column; and a condensing chamber coupled to said water column,said condensing chamber adapted to collect the condensed steam aspurified water.
 24. The water purification device of claim 23 whereinsaid heat source comprises a reflective parabolic conic surface adaptedto concentrate solar power, said heat source further comprising acentral apex line to tracks the azimuthal position of the sun so as toconcentrate sunlight onto said water column.
 25. The water purificationdevice of claim 24 wherein said reflective parabolic conic surfacecomprises increased altitude of said central apex line to track thealtitude position of the sun above the horizon.
 26. The waterpurification device of claim 23 wherein said compressor comprises aplurality of disks each of said plurality of disks comprising aplurality of enclosed spiral gas channels of increasing radii anddecreasing channel bore area as the radii turn, such that a gas can becompressed by an outside of said plurality of enclosed spiral gaschannels so as to push gas towards a center of compressor.
 27. The waterpurification device of claim 26 further comprising a disk motor withmagnetic rotors with axial magnetization and polygonal solenoid statorsto provide power to said compressor.
 28. The water purification deviceof claim 23 wherein said heat source comprises: a solar water heaterwith a plurality of tubes adapted to contain water and coupled with saidwater column, said tubes comprising partially vacuumed transparent tubesadapted to trap solar heat.